Proven research output on the behavior of structures made of waste copper slag concrete can improve its utilization in the construction industry and thereby help to develop a sustainable built environment. Although numerous studies on waste copper slag concrete can be found in the published literature, no research has focused on the structural application of this type of concrete. In particular, the variability in the strength properties of waste copper slag concrete, which is required for various structural applications, such as limit state design formulation, reliability-based structural analysis, etc., has so far not attracted the attention of researchers. This paper quantifies the uncertainty associated with the compressive-, flexural- and split tensile strength of hardened concrete with different dosages of waste copper slag as fine aggregate. Best-fit probability distribution models are proposed based on statistical analyses of strength data generated from laboratory experiments. In addition, the paper presents a reliability-based seismic risk assessment of a typical waste copper slag incorporated reinforced concrete framed building, considering the proposed distribution model. The results show that waste copper slag can be safely used for seismic resistant structures as it results in an identical probability of failure and dispersion in the drift demand when compared with a conventional concrete building made of natural sand.